Integral representations of the Riemann zeta function of odd argument
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910678447554560 |
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| author | Pain, Jean-Christophe |
| author_facet | Pain, Jean-Christophe |
| contents | In this article we obtain, using an expression of the digamma function $ψ(x)$ due to Mikolas, integral representations of the zeta function of odd arguments $ζ(2p+1)$ for any positive value of $p$. The integrand consists of the product of a polynomial by one or two elementary trigonometric functions. Examples for the first values of the argument are given. Some of them were already derived by other methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integral representations of the Riemann zeta function of odd argument Pain, Jean-Christophe Number Theory In this article we obtain, using an expression of the digamma function $ψ(x)$ due to Mikolas, integral representations of the zeta function of odd arguments $ζ(2p+1)$ for any positive value of $p$. The integrand consists of the product of a polynomial by one or two elementary trigonometric functions. Examples for the first values of the argument are given. Some of them were already derived by other methods. |
| title | Integral representations of the Riemann zeta function of odd argument |
| topic | Number Theory |
| url | https://arxiv.org/abs/2410.23096 |